Introduction to Behavioral Statistics Measurement The assignment of numerals to objects or events...

Introduction to Introduction to Behavioral StatisticsBehavioral Statistics

Introduction to Introduction to Behavioral StatisticsBehavioral Statistics

MeasurementMeasurement

The assignment of numerals to objects or The assignment of numerals to objects or events according to a set of rules. events according to a set of rules.

The rules used define or determine the The rules used define or determine the Level of MeasurementLevel of Measurement..

MeasurementMeasurement:

Levels of MeasurementLevels of Measurement - -

Nominal Level of Measurement Ordinal Level of Measurement Interval Level of Measurement Ratio Level of Measurement



Nominal Level of Measurement

The use of numbers or numerals as labels for a category ..



Ordinal Level of Measurement

The use of numbers or numerals to indicate rank order.



Interval level of Measurement

Interval scales have all of the propertiesInterval scales have all of the propertiesof ordinal scales, and in addition, equal of ordinal scales, and in addition, equal intervals on the scale of measurement intervals on the scale of measurement represent empirically equal intervals.represent empirically equal intervals.

Zero point is arbitary, Zero point is arbitary, notnot absolute! absolute!



Ratio level of Measurement

Ratio level scales have all of the propertiesRatio level scales have all of the propertiesof interval scales and in addition have anof interval scales and in addition have anabsolute zero point.absolute zero point.

Ratios are equal throughout the scale.Ratios are equal throughout the scale.



Nominal Level of Measurement Ordinal Level of Measurement Interval Level of Measurement Ratio Level of Measurement

Frequency Distributions and Graphs

Exact Limits are from: 49.5 - 59.5Exact Limits are from: 49.5 - 59.5

Frequency Distributions & Frequency Distributions & GraphsGraphs

Conventions for Frequency Distributions

– No more than 20 or fewer than 10 class intervals.

– Preferred class interval sizes (1,2,3,5,10,15,20).

– Start grouping so that the lowest class interval is a multiple of the class interval size.


Histogram

IQ Test Results from 5th Grade Class

012345678

50-5960-6970-7980-8990-99100-109110-119120-129130-139140-149150-159

Frequency Distributions and Frequency Distributions and GraphsGraphs

IQ Test Results from 5th Grade Class

012345678

50-59

60-69

70-79

80-89

90-99

100-109

110-119

120-129

130-139

140-149

150-159

Rules for Constructing a Histogram– Plot the graph over the

actual class limits (Exact Upper & Lower)

– Plot the Dependent Variable on the ordinate


Line Graph/Frequency Polygon Line Graph/Frequency Polygon

IQ Results from 5th Grade Class

012345678

50-59

70-79

90-99

110-119

130-139

150-159



012345678

50-59

70-79

90-99

110-119

130-139

150-159

Rules for Constructing a Frequency Polygon

– The point is placed over the mid-point of the class interval.

• Mid-point=UL-LL/2

– We assume that the interval above & below the highest and lowest class intervals are zero.

– To smooth a frequency polygon use:

• FS=X1+X2+X2+X3/4

– Start the Lowest class interval on the left side of the graph



0 2 4 6 8

50-59

70-79

90-99

110-119

130-139

150-159


50-59

70-79

90-99

110-119

130-139

150-159

0

2

4

6

8



IQ Results from 5th Grade Class50-5960-6970-7980-8990-99100-109110-119120-129130-139140-149150-159


What can I learn from a graph?What can I learn from a graph?


Clustering of scores around some central value.

Knowledge of the dispersion of scores around a central point.

Symetry or lack of symetry (skewness) Flatness or steepness of a distribution

(Kurtosis) Whether or not the distribution is bimodal.


This ends this unit! Please read the This ends this unit! Please read the section from your text discussing the section from your text discussing the use of the computer.use of the computer.

In our next unit, we will start putting In our next unit, we will start putting the peaces together by looking at the peaces together by looking at descriptive statistics……..descriptive statistics……..

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Introduction to Behavioral Statistics Measurement The assignment of numerals to objects or events...

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